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Levelling - A Practical Guide

Introduction
Levelling, in land surveying terms, is the process of determining the difference in height between two points in space.  This guide takes you through the basic concepts and theory, and then takes a step-by-step approach to demonstrating and explaining the practicalities.


Some concepts defined


Horizontal and Vertical


This guide will use the terms vertical and horizontal throughout so we must first define these concepts. Both vertical and horizontal are defined by reference to the Earth’s gravitational field, which for the purposes of this explanation is assumed to be constant.

Diagram explaining horizontal and vertical A vertical line between two points will be one that will pass through both points and continue to the centre of the Earth as defined by gravity. For instance, a string that is attached to a fixed point at one end and has a free moving weight attached at the other will describe a vertical line as the weight is pulled towards the Earth’s centre by gravity.


A horizontal line is a line that is perpendicular to a vertical line, and if long enough would circle the Earth at a constant distance from its centre.

Height/Level

Height, in this context, isn’t how tall something is but the vertical distance between a point in space and a fixed datum. The fixed datum is usually taken to be mean sea level where absolute values are required, such as in engineering works or map-making, but could be any arbitrary point if only relative values are required, such as in local drainage works. A more appropriate term for height is level.
In the UK, the mean sea level is defined by the Newlyn Tidal Observatory in Cornwall - see http://www.ntslf.org/tgi/newlyn-tidal-observatory for more details.


Precision and Accuracy

Precision
No distance in the real word can be measured exactly, but it can be measured to an appropriate precision. For example, it would be nonsense to state that the distance from London to Paris is 342,806.457metres. Saying that the distance from London to Paris is 840Km would be more appropriate. This is because the positions of London and Paris are vague and cannot be defined to millimetre precision, stating the distance to the nearest 10 kilometres is a more appropriate level of precision. By refining our definitions of London and Paris we could increase our by precision so we could say the distance from the centre of London to the centre of Paris is 342.8Km, i.e. to the nearest hundred metres.
The level of precision used when levelling will depend upon the requirements of the project. Civil Engineering works will require millimetre precision; drainage works may be less. “Precision Levelling”, to sub-millimetre precision, and requiring specialist equipment is beyond the scope of this guide.


Accuracy
Accuracy can be thought of as the effect of errors on the result of a measurement. There are many sources of errors during the levelling process but their effects can be greatly reduced by following the procedures below. A table of error sources, their impact and avoidance is included towards the end of this guide.

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